This statistic comes from a study by EyeView on various ecommerce sites.

In the study, two different variations of the same website were built, with 50% of the traffic being directed to a landing page with an embedded video, the other 50% directed to a page without.

The website that achieved the largest conversion rate (86%) was an online tutoring service. This is clearly the type of company that would naturally benefit from a landing page video, as most of its content is likely to be delivered via that medium anyway. It’s a free ‘sampler’, a way to show how professional and useful your service is before the visitor has signed up for a subscription.

Video is one of the best and most persuasive of all visual tools as it’s capable of delivering large amounts of information quickly and succinctly. Especially if it's about a new service or product.